### Abstract

The generalized Steiner tree problem is defined as follows. Given a graph with non-negative weights and a set of pairs of vertices find the minimum network of edges such that each pair of vertices is in the same connected component. We present an algorithm for the on-line Generalized Steiner Tree (GST) problem, and two other problems: Rectilinear Steiner Arborescence (RSA) and Symmetric Rectilinear Steiner Arborescence (SRSA). For each of these problems we provide polynomial time algorithms with performance ratios of O(log n). The constant factors hidden in the O-notation are small, in the case of the GST, we are within factor 2 from the proven lower bound. The previous best on-line GST algorithm (Awerbuch et at. [2]) was O(log^{2} n) competitive.

Original language | English (US) |
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Pages (from-to) | 344-353 |

Number of pages | 10 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

State | Published - Jan 1 1997 |

Event | Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA Duration: May 4 1997 → May 6 1997 |

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### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*, 344-353.

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*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*, pp. 344-353.

**On-line algorithms for Steiner tree problems.** / Berman, Piotr; Coulston, Chris.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - On-line algorithms for Steiner tree problems

AU - Berman, Piotr

AU - Coulston, Chris

PY - 1997/1/1

Y1 - 1997/1/1

N2 - The generalized Steiner tree problem is defined as follows. Given a graph with non-negative weights and a set of pairs of vertices find the minimum network of edges such that each pair of vertices is in the same connected component. We present an algorithm for the on-line Generalized Steiner Tree (GST) problem, and two other problems: Rectilinear Steiner Arborescence (RSA) and Symmetric Rectilinear Steiner Arborescence (SRSA). For each of these problems we provide polynomial time algorithms with performance ratios of O(log n). The constant factors hidden in the O-notation are small, in the case of the GST, we are within factor 2 from the proven lower bound. The previous best on-line GST algorithm (Awerbuch et at. [2]) was O(log2 n) competitive.

AB - The generalized Steiner tree problem is defined as follows. Given a graph with non-negative weights and a set of pairs of vertices find the minimum network of edges such that each pair of vertices is in the same connected component. We present an algorithm for the on-line Generalized Steiner Tree (GST) problem, and two other problems: Rectilinear Steiner Arborescence (RSA) and Symmetric Rectilinear Steiner Arborescence (SRSA). For each of these problems we provide polynomial time algorithms with performance ratios of O(log n). The constant factors hidden in the O-notation are small, in the case of the GST, we are within factor 2 from the proven lower bound. The previous best on-line GST algorithm (Awerbuch et at. [2]) was O(log2 n) competitive.

UR - http://www.scopus.com/inward/record.url?scp=0030676109&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030676109&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0030676109

SP - 344

EP - 353

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

SN - 0734-9025

ER -